Question

graph the image of △abc after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify the coordinates of $\triangle ABC$

Assume $A(-2, 2)$, $B(2, 2)$, $C(-2, 1)$.

Step2: Apply the dilation formula

For a dilation centered at the origin with scale - factor $k = 4$, the formula to find the new coordinates $(x',y')$ of a point $(x,y)$ is $(x',y')=(k\cdot x,k\cdot y)$.
For point $A(-2,2)$:
$x_A'=4\times(-2)= - 8$, $y_A'=4\times2 = 8$, so $A'(-8,8)$.
For point $B(2,2)$:
$x_B'=4\times2=8$, $y_B'=4\times2 = 8$, so $B'(8,8)$.
For point $C(-2,1)$:
$x_C'=4\times(-2)=-8$, $y_C'=4\times1 = 4$, so $C'(-8,4)$.

Step3: Graph the new triangle

Plot the points $A'(-8,8)$, $B'(8,8)$ and $C'(-8,4)$ on the coordinate - plane and connect them to form $\triangle A'B'C'$.

Answer:

Graph $\triangle A'B'C'$ with $A'(-8,8)$, $B'(8,8)$ and $C'(-8,4)$ on the given coordinate - plane.